1. Field of the Invention
The present invention relates to a three-dimensional image display apparatus, and more particularly, to an apparatus for displaying three-dimensional image data by using a numerical projection method (also called a reprojection method).
2. Description of the Related Art
As methods of stereoscopically displaying three-dimensional images, a surface shading method, a wire frame display method, a cross-section transformation method, a numerical projection display method, and the like are available. The surface shading display method and the wire frame display method are suitable to express a stereoscopic surface shape of an object. The cross-section transformation display method and the numerical projection display method are suitable to express a stereoscopic internal structure of an object. A conventional apparatus using the numerical projection method as the stereoscopic display method of MRI angiography, based on the fact that the numerical projection method is suitable to express a stereoscopic internal structure, is disclosed in C. L. Dumoulin, S. P. Souza, M. F. Walker, and W. Wagle, "Three-Dimensional Phase Contrast Angiography," Magnetic Resonance in Medicine 9, 139-148 (1989). In this case, a projection image of an anglogram is displayed as three-dimensional volume data obtained by a three-dimensional MRI procedure.
A projected image is formed in the following manner. A projection plane is set at an arbitrary position with respect to three-dimensional image data. Projection rays are caused to extend from an imaginary plane parallel to the projection plane toward the projection plane so that a projected image is formed on the projection plane by using the integral values, maximum values, or standard deviations of pixels on the rays as projection values. Each projection ray is caused to sequentially extend from the imaginary plane by a predetermined unit vector, and a pixel value on the projection ray is obtained at each position where the projection ray is incident on the three-dimensional image data, i.e., at the leading end of the sequentially extended projection ray.
Assume that the length of the unit vector coincides with the pitch of the pixel arrangement of the three-dimensional image data; that the projecting direction, a pixel arrangement direction (x, y, or z) of the three-dimensional image data; and that the distance from the imaginary plane to a pixel of the three-dimensional image data, which is closest to the imaginary plane is an integer multiple of the length of the unit vector. In this case, the pixels on the projection rays can be directly obtained by using the pixels of the three-dimensional image data. Otherwise, the pixels on the projection rays must be obtained from the three-dimensional image data by interpolation.
Assume that the projecting direction crosses the arrangement direction at a small angle. In this case, upon interpolation, the interpolated pixel value arrangement on the projection rays crosses the pixel value arrangement of the three-dimensional image data. As a result, these pixel value arrangements interfere with each other and moire (stripe artifact) may occur. The direction (longitudinal or lateral direction) of this moire is determined depending on whether the projection plane is rotated about the x-, y-, or z-axis to be inclined. Moire is not conspicuous much when the inclination angle of the projection angle of the projection direction is large (20.degree. to 45.degree.) but is conspicuous when the inclination angle is small (10.degree. or less).
Since an image is obscured by such moire, it is desirable that moire be removed in any case. If moire occurs in the above-mentioned image for medical purposes, diagnosis cannot be performed. For this reason, it is especially required to minimize moire in such a medical image.